The zagreb indices for chains and rings for cycles

In this paper, we find the first and second Zagreb indices for chains of cycles connected to vertices or edges and rings of cycles connected to vertices or edges, the first zagreb is the summation of the vertices degree, the second zagreb is the multiplication of the vertices degree, the number of edges that connected to vertex are the degree of vertex, we use the even cycles which are consist of even number of vertices, the number of vertices in the cycle are equal to edges while in the path the number of edges are less than the number of vertices (v#x003D;e -1) there is no edge that connected the first vertex with the last one while in cycle every vertex connected by edge with other vertix and then give some examples